[GitHub] [incubator-tvm] hzfan edited a comment on pull request #6771: [ARITH] Tight bound for floormod

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hzfan edited a comment on pull request #6771:
URL: https://github.com/apache/incubator-tvm/pull/6771#issuecomment-717639785


   @tqchen  The ir (before narrowing) is like
   ```
   for (ax0.ax1.fused.ax2.outer.fused: int64, 0i64, 42i64) "parallel" {
     for (n.oc_chunk.fused.oh.outer.fused: int64, 0i64, a_very_long_upper_bound) {
       ...
       ...
       for (oh.inner: int32, 0, 2) {
         for (ow.inner: int32, 0, 14) {
           for (oc_block: int32, 0, 16) "vectorized" {
             ...floormod(n.oc_chunk.fused.oh.outer.fused, cast(int64, floordiv(((cast(int32, ((floormod(ax0.ax1.fused.ax2.outer.fused, 7i64)*2i64) + 1i64)) + 1) - cast(int32, (floormod(ax0.ax1.fused.ax2.outer.fused, 7i64)*2i64))), 2)))...
           }
         }
       }
     }
   }
   ```
   Let `a = n.oc_chunk.fused.oh.outer.fused` (the first operand of floormod), `b = cast(int64, floordiv(((cast(int32, ((floormod(ax0.ax1.fused.ax2.outer.fused, 7i64)*2i64) + 1i64)) + 1) - cast(int32, (floormod(ax0.ax1.fused.ax2.outer.fused, 7i64)*2i64))), 2))` (second operand of floormod)
   `const_int_bound` gives `0 <= a <= 6` and `-5 <= b <= 7`.
   
   In a simplified form, 
   ```
   b = floordiv(c * 2 + 2 - c * 2, 2), where
   c = floormod(ax0.ax1.fused.ax2.outer.fused, 7)
   ```
   
   I guess `c * 2 + 2 - c * 2` is not simplified as `2`, instead, its bound is analyzed directly, so the min becomes negative due to the minus operation.


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